Article pubs.acs.org/JAFC
Modeling Real-Time PCR Kinetics: Richards Reparametrized Equation for Quantitative Estimation of European Hake (Merluccius merluccius) Ana Sánchez,*,† José A. Vázquez,‡ Javier Quinteiro,§ and Carmen G. Sotelo† †
Grupo de Bioquı ́mica de Alimentos and ‡Grupo de Reciclado e Valorización de Residuos (REVAL), Instituto de Investigacións Mariñas (CSIC), C/Eduardo Cabello 6, 36208 Vigo, Spain § Departamento de Bioquı ́mica e Bioloxı ́a Molecular, Facultade de Bioloxı ́a, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain S Supporting Information *
ABSTRACT: Real-time PCR is the most sensitive method for detection and precise quantification of specific DNA sequences, but it is not usually applied as a quantitative method in seafood. In general, benchmark techniques, mainly cycle threshold (Ct), are the routine method for quantitative estimations, but they are not the most precise approaches for a standard assay. In the present work, amplification data from European hake (Merluccius merluccius) DNA samples were accurately modeled by three sigmoid reparametrized equations, where the lag phase parameter (λc) from the Richards equation with four parameters was demonstrated to be the perfect substitute for Ct for PCR quantification. The concentrations of primers and probes were subsequently optimized by means of that selected kinetic parameter. Finally, the linear correlation among DNA concentration and λc was also confirmed. KEYWORDS: real-time PCR, hake, Merluccius merluccius identification, DNA quantification, mathematical modeling, Richards equation
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different presentations (such as tails, loins, and fillets). Nowadays, some of these species (South African and silver hake) can also be found fresh in European markets. Because M. merluccius is the most appreciated species within the Merluccius genus and because its market value is higher than that of the other species, some mislabeling or fraud might occur. Therefore, this is a clear example in which the application of real-time PCR would be required to verify seafood species. In recent years an increasing number of methods for DNA data modeling and software associated with the evaluation of real-time PCR results have been reported.19−21 However, the most common method used to analyze the experimental data is based on the threshold cycle method. It uses a fluorescence threshold value (Ct) within the exponential phase of the amplification curve as benchmark, wherein all of the samples reached the same fluorescence signal, that is, they have the same amount of amplified product but achieved in different reaction cycles.22 The Ct method is dependent on the subjectivity to establish randomly the Ct value in any point of the exponential phase from the fluorescence cycle curve. This is because the comparison of data from different assays is not feasible. This problem limits, in many cases, the reliability of quantitative PCR causing infra- or overestimation errors in the determination of DNA concentration. Thus, the analysis of data from real-time PCR is far from being standardized among different laboratories, equipments, or technicians.
INTRODUCTION The main applications of real-time PCR were directed toward the field of medicine, in particular to gene expression, cancer diagnosis, autoimmune diseases, or identification and quantification of pathogens.1−4 Nowadays, this technique is also used in other fields, such as food technology,5 for which it is an essential tool for the detection and quantification of genetically modified organisms (GMO). Another prominent application of this technique, in the food technology area, is species identification, mainly for food products that do not allow morphological identification of the animal or plant food component.6−11 In the case of seafood, species identification has been addressed through several DNA techniques such as restriction fragment length polymorphism (RFLP), single-strand conformation polymorphism (SSCP), or forensically informative nucleotide sequencing (FINS).12,13 However, these methodologies are less effective in the analysis of products in which several species are present. Therefore, it is necessary to apply other techniques, such as real-time PCR, which can resolve this casuistry in a fast, easy, and cheap way.14−16 Additionally, labeling rules for mandatory declaration of the amount of certain ingredients in foods (EU directive 2000/13/EG) require tools for their identification and quantification. Reports related to species quantification in foods that do not use realtime PCR are quite scarce and always semiquantitative.17,18 However, real-time PCR seems to be the most suitable method for quantitative purposes. Spanish markets have traditionally sold the commercial fish species Merluccius merluccius (European hake) mostly as a fresh whole fish, whereas other species belonging to the same family (Merluccidae) are often marketed as frozen products with © 2013 American Chemical Society
Received: Revised: Accepted: Published: 3488
January 11, 2013 March 11, 2013 March 13, 2013 March 13, 2013 dx.doi.org/10.1021/jf400136j | J. Agric. Food Chem. 2013, 61, 3488−3493
Journal of Agricultural and Food Chemistry
Article
Table 1. Equations Used To Model the Real-Time PCR Data Obtained from Hake DNA Analysisa
Definition of parameters is also summarized: F, fluorescence; Fm, maximum fluorescence; C, amplification cycle number; b, cycle number to achieve the semimaximum fluorescence; μ, specific maximum rate of fluorescence increment; C50, cycle number to achieve the semimaximum fluorescence; λC, lag phase or number of cycles necessary to detect fluorescence in the amplification process; α, position parameter of Weibull equation; β, form parameter of Weibull equation and related to maximum slope of the fluorescence; μ*, specific apparent maximum rate of fluorescence increment; C*, position parameter of Richards equation (with four parameters); a, form parameter of Richards equation and related to maximum slope of the fluorescence. a
An alternative is to adjust the fluorescence data obtained throughout the amplification process (number of cycles) using a suitable mathematical model.23,24 Nonlinear profiles are easily modeled by sigmoid equations that produce an absolute prediction of PCR kinetics. Different models have been used (Gompertz, logistic, Hill, Chapman, etc.), almost always getting good descriptions of the experimental patterns.25,26 In this last work, the authors propose a very consistent parameter (Cy0) to replace the use of Ct. However, the equation of five parameters defined by Guescini et al.26 is not reparametrized for Cy0 with the subsequent difficulty to calculate the confidence intervals and corresponding comparison between samples by statistical tests. However, mathematical modeling of real-time PCR amplification curves from seafood DNA has never been reported. The aim of the present work was to compare the capacity and goodness of fit from three sigmoid and reparametrized equations (logistic, Weibull, and Richards) to model the realtime PCR data from hake (M. merluccius) samples. A significant parameter, λc, from Richards’ equation was studied as an alternative to substitute the common and most random Ct parameter. Finally, the primers and probe concentrations for the MMER_VIC system15 were optimized using λc values.
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Real-Time PCR System and Reaction Conditions. The evaluated real-time PCR system was a Taqman-MGB species-specifc system for M. merluccius (MMER_VIC) designed in a previous work.15 The sequences of the primers and probe are as follows: MMERCR4F (forward), 5′-CATTYTCYTATATTAACCATTCAGGCAAT-3′; MMERCR5R (reverse), 5′-TGGGTTGACAGGTTAAATACGAGTAA-3′; and MMERCR6TP (probe), 5′-AGAACATTAACATAAAATTAAACT-3′. The 5′ end of the probe was labeled with the fluorescent reporter dye VIC, and the minor groove binding (MGB) was located at the 3′ end. PCR reactions were performed in a total volume of 20 μL in a MicroAmpTM fast optical 96-well reaction plate (Applied Biosystems), covered with MicroAmpTM optical adhesive film (Applied Biosystems). Each reaction contained 25 ng of DNA, 10 μL of TaqMan Fast Universal PCR Master Mix UNG Amperase (2×). The final forward and reverse primer concentration was 900 nM, 225 nM being the probe concentration. Reactions were run on an ABI 7500 Fast (Applied Biosystems) with the standard thermal cycling protocol: 95 °C for 10 min followed by 40 cycles of 95 °C for 15 s and 60 °C for 1 min. On the other hand, the optimization experiments of forward and reverse primers were performed at 50, 300, and 900 nM. Mathematical Models. Three sigmoid equations (Table 1) were evaluated to model the profiles of fluorescence versus cycle number of PCR amplification. The selected equations are well-known and applied in a wide range of chemical and biological contexts.23,24,27−30 The formulation of these equations with parameters of clear geometrical and biological meaning (Figure 1 and Table 1) facilitates the perfect description and classification of the experimental tendencies. In addition, the fittings using reparametrized functions help to calculate easily the confidence intervals of the mentioned coefficients. The algebraic steps required to obtain them are described, for the most complex equation (Richards), in the Supporting Information. Numerical and Statistical Methods. The fitting procedures and parametric estimates from the experimental results were performed by minimizing the sum of quadratic differences between the observed and model-predicted values using the nonlinear least-squares (quasiNewton) method provided by the Solver macro from the Microsoft Excel spreadsheet. The confidence intervals of the best-fit values for the parametric estimates (Student t test; α = 0.05), consistency of the mathematical models (Fisher’s F test; p < 0.05), and covariance and correlation matrices were calculated using the SolverAid macro, which is freely available from Levie’s Excellaneous Web site: http://www. bowdoin.edu/∼rdelevie/excellaneous/.
MATERIALS AND METHODS
DNA Extraction. DNA was isolated from 0.15−0.2 g of frozen or ethanol-preserved muscle from 10 samples of M. merluccius and 5 samples of other Merlucciidae species. Tissue disruption and protein digestion were performed in a thermoshaker at 56 °C with 860 μL of lysis buffer (1% SDS, 150 mM NaCl, 2 mM EDTA, 10 mM Tris-HCl, pH 8), 100 μL of guanidium thiocyanate (5 M), and 40 μL of proteinase K (>20 units/mg). Extra proteinase K (40 μL) was added to each sample after 3−4 h and left overnight. After digestion, DNA was isolated by employing the Wizard DNA Clean-Up System kit (Promega) by following the manufacturer’s instructions. The eluted DNA was quantified by UV spectrometry at 260 nm and with a QuantiT PicoGreen dsDNA Assay Kit (Invitrogen) for dsDNA quantification in a VersaFluor Fluorometer (Bio-Rad). DNA concentration was adjusted to 12.5 ng/μL for subsequent RT-PCR reactions. 3489
dx.doi.org/10.1021/jf400136j | J. Agric. Food Chem. 2013, 61, 3488−3493
Journal of Agricultural and Food Chemistry
Article
Table 2. Parametric Estimates and Confidence Intervals (α = 0.05) from the Equations Summarized in Table 1 Applied to the Real-Time PCR Data Obtained by the MMER_VIC Systema parameter
Figure 1. Graphical description of the kinetic parameters Fm, λc, and C50 from a typical sigmoid curve. The line tangent at the inflection point of the sigmoid (R) and Fm/2 are also shown.
eq 1
eq 2
eq 3
Fm μ C50 λc α β μ* C* a
1.55 ± 0.06 0.28 ± 0.03 25.48 ± 0.52 18.44 ± 0.69
1.54 ± 0.06
1.67 ± 0.08
25.59 ± 0.52 18.01 ± 0.70 27.60 ± 0.65 4.84 ± 0.50
25.81 ± 0.50 17.73 ± 0.44
R2adj F ratio p value
0.9925 1602.5
